Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve an exponential equation by isolating the exponential factor and taking logarithms
Problem
Describe the most efficient method for solving \(2^{x~+~1}~=~64\) and justify why it applies.
Big Picture
What this problem is really about
Method comes before machinery here. Check whether the constant is an exact power of the base already present; if it is, rewrite both sides with that base and use one-to-one behavior to equate exponents. Logarithms remain a valid general method, but the common-base route is exact and more direct.
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